Roman Numeral Converter
runs in your browserConvert numbers to Roman numerals and back. Strict checking names the rule a numeral breaks, and the overline notation carries on past 3999.
Digits are turned into a numeral, letters into a number. Standard form covers 1 to 3,999; above that a bar over a group (the vinculum) multiplies it by a thousand.
The seven letters
| I | 1 | a single tally stroke |
| V | 5 | an open hand, or the top half of X |
| X | 10 | two crossed tally strokes |
| L | 50 | a flattened Etruscan sign |
| C | 100 | centum, a hundred |
| D | 500 | half of the old CIↃ for a thousand |
| M | 1,000 | mille, a thousand |
I, X, C and M repeat up to three times; V, L and D never do. Only I, X and C may sit before a larger letter to subtract, and only from the next two values up.
about this tool
The rules, all of them
Roman numerals use seven letters — I, V, X, L, C, D, M for 1, 5, 10, 50, 100, 500, 1000 — written from largest to smallest and added up. Three rules turn that into the standard form found in every reference book. I, X, C and M repeat at most three times in a row; V, L and D never repeat, because two of them are simply the next letter. A smaller letter before a larger one subtracts, but only I, X and C may do it, and only from the next two values up: IV, IX, XL, XC, CD, CM. And each place — ones, tens, hundreds, thousands — is written once, so a numeral is really four short groups side by side: MCMXCIV is M, CM, XC, IV, or 1000 + 900 + 90 + 4.
The tool applies those rules strictly when it reads, and when a numeral fails it names the rule: VV is refused because two Vs make X, IIX because nothing as large as X may follow II, IL because I may only sit before V or X. "Invalid" on its own teaches nothing.
IIII and other old habits
The additive form — IIII for 4, XXXX for 40 — is older than the subtractive one and survives on clock faces, where it balances VIII on the opposite side of the dial, and in some inscriptions. It is not wrong, just not standard, so it is refused by default and accepted with lenient reading on, which also tells you the standard spelling. Lowercase letters (mcmxc) and the dedicated Unicode numeral characters (Ⅻ) are read without complaint, with a note that says what happened.
Past 3999
Standard form runs out at MMMCMXCIX. The convention for larger numbers, used from the Middle Ages onwards, is a bar over a group of letters — the vinculum — multiplying the group by a thousand. This tool writes it with the Unicode combining overline, so 4000 comes out as I̅V̅ and 1 000 000 as M̅, and reads it back whether the bar is a combining overline, a macron or a spacing overline character. The notation reaches 3 999 999; there is no accepted way to write anything larger.
Zero, negatives, fractions
There is no numeral for zero: the system counts things, and none of them is not a count. Medieval scribes writing tables occasionally used N, for the Latin nulla, but it never joined the notation. Negatives and fractions have no standard form either — the Romans had a duodecimal fraction system based on the uncia (a twelfth) with its own symbols, which this tool does not attempt.
Limits
Reading is strict by default, so the many non-standard forms seen in the wild — IIIIII, XIIX, MDCCCCX — are refused with a reason rather than guessed at. Lenient mode adds only the four-in-a-row additive forms; it does not accept a subtractive pair in the wrong place. Number input takes whole numbers with optional thousands separators; anything with a decimal point is refused.
For the bases a computer actually uses, the number base converter covers 2 to 36. Text to binary, Morse & more handles the other historical encodings.
questions
- What are the rules for writing Roman numerals?
- Seven letters — I 1, V 5, X 10, L 50, C 100, D 500, M 1000 — written largest first and added up. I, X, C and M may repeat up to three times; V, L and D never repeat. A smaller letter placed before a larger one subtracts, but only six such pairs exist: IV, IX, XL, XC, CD and CM. Each place (ones, tens, hundreds, thousands) is written once.
- Why do clock faces show IIII instead of IV?
- Tradition rather than arithmetic. IIII balances the VIII opposite it on the dial, it avoided a monogram of the god Jupiter (IV in Latin spelling) in Roman times, and a clockmaker casting numerals could pour the whole dial from one mould of twenty Is, four Vs and four Xs. Turn on lenient reading to accept it.
- How are numbers above 3999 written?
- Standard form stops at MMMCMXCIX. Medieval and early modern writers put a bar, the vinculum, over a group of letters to multiply it by a thousand, so V̅ is 5000 and X̅ is 10 000. This tool writes and reads that notation, which reaches 3 999 999.
- Is there a Roman numeral for zero?
- No. The system counts things, and there is no numeral for none of them. Medieval scribes occasionally wrote N, for the Latin nulla, in tables, but it never became part of the notation. Negatives and fractions have no standard numerals either.
- Why does it reject IIX or VX?
- Because they break the subtraction rule. Only I, X and C may be placed before a larger letter, and only before the next two values up: I before V or X, X before L or C, C before D or M. IIX, VX, IL, IC and IM are all invalid; the tool tells you which rule each one breaks rather than saying "invalid".